If you have enough hose on the heater then you should be able to leave the hoses hooked up take it loose however it is mounted and tie wire/zip tie, or some string to hold it out of the way. Do your thing and put it back. If you need to disconnect the hoses then there are several ways that have been discussed but as a refresher if you would post a pic of your specific heater then we can give problem specific ideas/opinions.

Big heater's out. Cut the hoses and wires shorter but keeping the smaller heater; I want to put it under my table for foot warming purposes (like a kotatsu kinda thing). It's out of the way right now and the hoses connected w copper elbow... de-rusting the floor now. I have like 4 box fans I dumpstered 3 months ago, I had plans on using them! lol

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ATTEMPT NO LANDING THERE

I removed every heater from my bus.
The coolant lines lead from the engine into the cab through the firewall.
First to the primary heater and pump, looped through the door heater, then back around the driver to the front, mid ship and rear heater.
My lines have valves built in and I just closed them and cut the lines.
Pulled all of the heaters and didn't have hardly any leakage.
I stood the rear heater up on end, cut the lines and bungee corded the lines to the top of the windows keeping all of the coolant in.
I carried the heaters out and drained into a bucket.
I used a shop vac and sucked the coolant out of the lines.
Then removed the mid ship heater and so on until I got the main heater out.
There was 5-6 gallons of coolant removed along with the heaters.
I gave the heaters to a buddy that hooked them up on his semi truck trailer.
So, that was my experience.

I removed every heater from my bus.
The coolant lines lead from the engine into the cab through the firewall.
First to the primary heater and pump, looped through the door heater, then back around the driver to the front, mid ship and rear heater.
My lines have valves built in and I just closed them and cut the lines.
Pulled all of the heaters and didn't have hardly any leakage.
I stood the rear heater up on end, cut the lines and bungee corded the lines to the top of the windows keeping all of the coolant in.
I carried the heaters out and drained into a bucket.
I used a shop vac and sucked the coolant out of the lines.
Then removed the mid ship heater and so on until I got the main heater out.
There was 5-6 gallons of coolant removed along with the heaters.
I gave the heaters to a buddy that hooked them up on his semi truck trailer.
So, that was my experience.

what do you do for road heat and defrosters? put in new units?

I replaced the guts out of my driver console heaters but re-used the cabinet.. they were totally nasty and shot... seems no one ever cleans the coils in the bus heaters...

I first took a line off under the hood and drained a lot of the oolant into a bucket then used the booster pump to pump a lot of the lines dry before I took the units out. my rear heater i kept but disassembled so I did as suggested and picked it up on end before I yanked the lines...